Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 670 · 40 sums

The method (Split into easy parts): (a + b)² = a² + 2ab + b². (a − b)² = a² − 2ab + b². (a + b)(a − b) = a² − b²; so a² − b² = (a + b)(a − b). a² + b² = (a + b)² − 2ab = (a − b)² + 2ab.

1. 1.If a + b = 4 and ab = 3, what is a² + b²?
2. 2.Use (a − b)² = a² − 2ab + b² to find 75².
3. 3.Use a² − b² = (a + b)(a − b) to find 42² − 16².
4. 4.Use (a + b)² = a² + 2ab + b² to find 82².
5. 5.Use (a + b)(a − b) = a² − b² to find 82 × 78.
6. 6.Use a² − b² = (a + b)(a − b) to find 67² − 61².
7. 7.Use a² − b² = (a + b)(a − b) to find 51² − 18².
8. 8.Use a² − b² = (a + b)(a − b) to find 47² − 28².
9. 9.Find the value of x² − 2xy + y² when x = 5 and y = 2.
10. 10.Use a² − b² = (a + b)(a − b) to find 56² − 39².
11. 11.Find the value of x² − y² when x = 4 and y = 3.
12. 12.Use (a − b)² = a² − 2ab + b² to find 71².
13. 13.If a + b = 5 and ab = 4, what is a² + b²?
14. 14.Use (a − b)² = a² − 2ab + b² to find 95².
15. 15.Use a² − b² = (a + b)(a − b) to find 74² − 28².
16. 16.Find the value of x² − 2xy + y² when x = 9 and y = 1.
17. 17.Find the value of x² − y² when x = 15 and y = 3.
18. 18.Use (a + b)² = a² + 2ab + b² to find 64².
19. 19.Find the value of x² + 2xy + y² when x = 9 and y = 7.
20. 20.Find the value of x² + 2xy + y² when x = 14 and y = 8.
21. 21.Find the value of x² − y² when x = 5 and y = 1.
22. 22.Find the value of x² − 2xy + y² when x = 13 and y = 2.
23. 23.If a − b = 2 and ab = 63, what is a² + b²?
24. 24.Use (a − b)² = a² − 2ab + b² to find 96².
25. 25.Find the value of x² − 2xy + y² when x = 11 and y = 3.
26. 26.Use a² − b² = (a + b)(a − b) to find 80² − 31².
27. 27.Use (a + b)(a − b) = a² − b² to find 34 × 26.
28. 28.Use (a − b)² = a² − 2ab + b² to find 82².
29. 29.Use (a + b)² = a² + 2ab + b² to find 55².
30. 30.Use (a − b)² = a² − 2ab + b² to find 47².
31. 31.Find the value of x² − 2xy + y² when x = 11 and y = 4.
32. 32.Use (a + b)² = a² + 2ab + b² to find 31².
33. 33.Use (a + b)(a − b) = a² − b² to find 76 × 64.
34. 34.If a + b = 17 and ab = 66, what is a² + b²?
35. 35.Use (a − b)² = a² − 2ab + b² to find 86².
36. 36.If a − b = 6 and ab = 16, what is a² + b²?
37. 37.Use a² − b² = (a + b)(a − b) to find 44² − 36².
38. 38.If a + b = 7 and ab = 10, what is a² + b²?
39. 39.Use (a − b)² = a² − 2ab + b² to find 35².
40. 40.Use (a − b)² = a² − 2ab + b² to find 38².

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